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C19×#63118⋊C3 #28414809

order14820
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×#63118⋊C3
unambiguous semidirect product#63118⋊(C3×C19)

Splittings

Fitting, socle, HallC5×C13×C19 ⋊ C3×C4
derived, HallC5×C13 ⋊ C3×C4×C19
HallC19×#63118 ⋊ C3
HallC5×C19×C13⋊C3 ⋊ C4
HallC19×C13⋊C3 ⋊ Dic5
Hall#63118 ⋊ C3×C19
HallC13×C19 ⋊ C3×Dic5
HallC5×C13⋊C3 ⋊ C4×C19
HallC5×C19 ⋊ AGL(1,𝔽13)
HallC13⋊C3 ⋊ C19×Dic5
SylowC13 ⋊ C3×C19×Dic5
SylowC5 ⋊ C19×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC19#63118⋊C3
commutator, hypocenterC5×C13C3×C4×C19
FrattiniC1G
Fitting, socleC5×C13×C19C3×C4
prime radicalC5×C19×D13⋊C3C2
cosocleC5×D13C2×C3×C19
LCSG ▷ C5×C13
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1235

Conjugacy classes & character table

551 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 95);